How do you make a torus 'telescope' open?
You could do this easily with a torus curve, if you dont mind the bezier curve object.

Just add a Bezier Curve Circle, make its handles Free type and erase the bottom half (or whichever suits your design).

Make it 2D type with None fill so it is like a torus.

Adjust the bevel radius and resolution as desired.
Add a Mirror modifier in the corresponding axis to mirror the animation.

You can now animate the aperture with the *Bevel Factor > Start and end factors.



Alternatively if symmetry is not your concern, you may simply turn the circle into an open shape by duplicating one of its vertex and erasing one segment, and then controlling both the Start and End Bevel Factor values independently.